MSSL SOLARNET School MHD Waves. Stephane REGNIER Northumbria University
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1 MSSL SOLARNET School 2016 MHD Waves Stephane REGNIER Northumbria University
2 MSSL SOLARNET School Definition of a wave 2. The three MHD waves a. Linearized MHD equations b. Dispersion relation c. Properties 3. MHD waves in different geometries a. Rectangular slab b. Cylinder 4. Solar observations of MHD waves 1. Slow modes 2. Fast modes 3. Alfvén modes
3 Definition of a wave MSSL SOLARNET School 2016
4 MSSL SOLARNET School 2016 The case of an electromagnetic wave: - The electric field and magnetic field are perpendicular - The wave is propagating along the direction perpendicular to the electric and magnetic fields - The propagation speed (phase speed) is the speed of light c Fig. 1: basic description of an electromagnetic wave
5 MSSL SOLARNET School 2016 A wave is defined by - The components of the electric field (polarisation, Stokes parameters) - The components of the magnetic field - The direction of the propagation or wave number - The dispersion relation: relation between the wavenumber and the angular frequency (see dispersion diagram) - The phase and group speeds - The perturbation of the thermodynamic quantities
6 MSSL SOLARNET School 2016
7 MSSL SOLARNET School 2016
8 MSSL SOLARNET School 2016
9 MHD waves MSSL SOLARNET School 2016
10 MSSL SOLARNET School 2016 The MHD equations are Linearized MHD equations
11 Linearized MHD equations MSSL SOLARNET School 2016
12 Linearized MHD equations MSSL SOLARNET School 2016
13 Linearized MHD equations MSSL SOLARNET School 2016
14 Linearized MHD equations MSSL SOLARNET School 2016
15 Linearized MHD equations MSSL SOLARNET School 2016
16 Dispersion relations MSSL SOLARNET School 2016
17 Dispersion relations MSSL SOLARNET School 2016
18 Dispersion relations MSSL SOLARNET School 2016
19 MSSL SOLARNET School 2016
20 MSSL SOLARNET School 2016
21 Some Properties MSSL SOLARNET School 2016
22 MSSL SOLARNET School 2016 Some Properties Magnetoacoustic waves - Phase speed varying with the angle of propagation - Group speed varying with the angle of propagation - Fast mode efficient to transport energy - Fast mode may have phase speed equal to Alfvén speed
23 MHD waves in different geometry MSSL SOLARNET School 2016
24 MSSL SOLARNET School 2016 Slab and Tube Geometry Wave in a non-uniform plasma - Two media: internal and external - Jump in density, temperature, magnetic field - Discontinuity at the interface - Total pressure balance - See for instance the Joarder and Roberts model
25 MSSL SOLARNET School 2016 Tube Geometry Surface and body modes - Generation of surface modes - Cylindrical coordinates - Bessel functions - Imposing boundary conditions to fully determine the waves properties
26 MSSL SOLARNET School 2016 Tube Geometry Representation of magnetoacoustic modes: sausage, kink and flute
27 MSSL SOLARNET School 2016 Some Properties Magnetoacoustic waves have different modes: sausage and kink
28 MSSL SOLARNET School 2016 Tube Geometry Dispersion diagram for coronal loop (coronal values)
29 MSSL SOLARNET School 2016 Tube Geometry Dispersion diagram for photosphere/chromosphere
30 Observations of waves MSSL SOLARNET School 2016
31 Slow modes Slow modes observed in coronal loops
32 MSSL SOLARNET School 2016 Fast kink modes Examples of fast modes generated by external sources such as flares
33 MSSL SOLARNET School 2016
34 MSSL SOLARNET School 2016
35 MSSL SOLARNET School 2016
36 Alfvenic modes MSSL SOLARNET School 2016
37 MSSL SOLARNET School 2016 Why to study waves? - Ubiquitous in the solar atmosphere - Transport of energy - Coronal heating - Chromospheric heating (reflection and transmission of waves) - Magnetic reconnection - Flares Not only MHD waves but also electronic and ionic plasma waves
38 MSSL SOLARNET School 2016 Instabilities Stephane REGNIER Northumbria University
39 1. Perturbation theory 2. Kink instability 3. Rayleigh-Taylor instability 4. Kelvin-Helmholtz instability 5. Thermal instability 6. Interchange instability
40 Perturbation Theory
41 Perturbation Theory
42 Perturbation Theory
43 Kink Instability Instability of a twisted flux tube exceeding a threshold of twist
44 Kink Instability
45 Rayleigh-Taylor Instability Two media with different thermodynamic and magnetic properties. No flow along x. z x Two cases: - Two plasmas with a uniform magnetic field - One plasma supported by magnetic field
46 Rayleigh-Taylor Instability
47 Rayleigh-Taylor Instability
48 Rayleigh-Taylor Instability
49 Kelvin-Helmholtz Instability Hydrodynamic instability with two media with different flows
50
51
52 Kelvin-Helmholtz Instability
53 Thermal Instability
54 Thermal Instability
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